1. Field of the Invention
The present invention relates to signal processing. More particularly, the invention relates to identification and recognition of particular features of signals or, more specifically, phase and frequency transitions within a signal.
2. Description of the Prior Art
Signal extraction is an increasingly growing field of signal processing that calls for recognition of certain events in a received signal. The event may be a particular pattern, or, as in the present invention, a signal or a portion thereof having a certain feature, such as a phase transition. Often, little is known about the received signal prior to receipt. In the present invention, it is specifically desired to know the existence of any phase transitions or frequency transitions contained within the signal. A phase transition is where the phase changes abruptly and either decreases or increases relative to a previous portion of the signal. Similarly, a frequency transition is where the frequency shifts, which is usually where the phase transitions. Recognition of phase transitions can be specifically problematic due to the short length of phase transitions, such that few data samples are associated with the phase transition, and the fact that noise often masks the phase transition. Data spikes and outliers also tend to skew the data or otherwise make signal extraction difficult.
Because the data samples associated with a phase transition may be very few, a technique that considers outlying data samples that deviate from the norm of the data samples associated with the phase transition tends to skew or otherwise exert heavy influence on the final extracted image. One prior art method of recognizing or extracting the phase transition is the zero-crossing method, which is discussed in J. Tsui, Digital Techniques for Wideband Receivers, SciTech Publishing, Inc., 2nd ed. 2004, Chpt. 9. The zero-crossing method is problematic, however, because it does not ignore or otherwise take into account outliers. Because the outliers are considered when extracting an image, the final extracted image may be inaccurate or otherwise negatively influenced.
A technique that considers too many data samples may be equally problematic, in that data samples outside the phase transition (or outside a zone around the phase transition) may introduce a negative influence. This is because such data samples may improperly contribute to the final extracted image.
Other prior art methods include a delta phase method, also discussed in Digital Techniques at page 330. FIG. 1, which is denoted as “prior art,” illustrates unwrapped phase values in the top graph and the average delta phase in the bottom graph. The delta phase method described in Digital Techniques computes the phase transition from the unwrapped phase. The delta phase is the next phase minus the present phase. To smooth the result, an average is obtained from four delta phases. Four is chosen so that it produces the best smoothing without compromising the resolution. A higher number gives a smoother result but broadens the peak. The absolute value of the average delta phase is shown, i.e., with the negative values rectified. Additionally, the DC level of the average delta phase is removed.
FIG. 2, also denoted as “prior art,” illustrates the unwrapped phase values in the top graph and a magnified result of the average delta phase method described in Digital Techniques. The plot of the bottom graph of FIG. 2 shows a broad peak and a less well-defined start and end of the phase transition.
Accordingly, there is a need for an improved method and computer program that overcomes the limitations of the prior art. More particularly, there is a need for a method and computer program that is not sensitive to outliers or an excessive number of data samples. There is further a need for a method and computer program operable to accurately extract phase transitions while ignoring noise that tends to degrade the extracted image.